In This paper, we give a necessary condition for function in L 2 with its DUAL to generate a DUAL SHEARLET tight FRAME with respect to admissibility.

Necessary conditions for SHEARLET and cone-adapted SHEARLET systems to be FRAMEs are presented with respect to the admissibility condition of generators.

In the Eccentric braced FRAMEs (EBFs), which one end of the link beam is connected to a column, the safety of the link-to-column connection is a requirement for the ductile and safe performance of the EBF. But among of the tests that have been implemented on this connection yet, because of the intensity of forces on vulnerable region of the link-to-column connection, the tested specimens were confronted with brittle and sudden failures. So it seems that the reduced beam section (RBS) can be a suitable solution for raising this problem, by concentrating flexural stresses at a location away from the connection, in flexural yielding link beams. Therefore in this paper, the possibility of keeping the plastic hinge away from the location of link-to-column connection, in the meanwhile achieving the required plastic rotation of link beam, by using the RBS connection, were investigated. This evaluation was done by using a finite element program ETABS and with nonlinear static analysis (pushover) for a DUAL system of special moment FRAME and special eccentric braced FRAME. According to the present work, the models with RBS by earlier developing the hinge at the RBS region, delay yielding occurrence of link at the column face. So the yielding does not occur at the column face, at least prior to achieving the moment at the location of RBS region to 1.1 times of its expected plastic moment capacity.

The most important characteristics of building FRAMEs can be abbreviated in stiffness, strength and ductility. Moment FRAMEs have ductile behavior and low stiffness; Therefore, the main reason in using the lateral bracing systems is their considerable stiffness. Eccentric bracing systems are considered as ductile FRAMEs, while satisfying the required stiffness. The lateral stiffness of conventional eccentric configurations have been calculated previously. In this research, the lateral relative stiffness of eccentrically braced FRAME with DUAL vertical links (EBF-DVL) is calculated analytically. EBF-DVL has two parallel vertical links which are welded to the floor beam at the top and to one horizontal link at the bottom. In order to provide the required equations for obtaining the stiffness, the slope-deflection equations are used by considering the effects of shear deformations. The results show that EBF-DVL has a high relative stiffness and by adjusting the lengths of vertical and horizontal links, it is possible to achieve the stiffness even more than the stiffness of eccentric bracing with horizontal link between two diagonal braces. Although an increase in either the moment of inertia or shear area of the vertical link leads to an increase in the lateral stiffness of the system, the effective interval for increasing the moment of inertia of the vertical links is to be limited to approximately half of the column moment of inertia and the corresponding value for increasing the shear area is approximately 60% of the shear area of the column.

Following a large earthquake, numerous aftershocks can be triggered due to the complex stress interaction between and within tectonic plates. Although aftershocks are normally smaller in magnitude, their ground motion intensity can be large and have different energy contents than the mainshock. Even seemingly, undamaged buildings may be damaged as a result of aftershocks. The mainshock-damaged buildings with deteriorated structural properties are more susceptible to damage. Based on the achievements of structural engineering and earthquake today, design of structures based on performance can be mentioned. Firstly, unlike traditional methods, new structures can be designed based on seismic needs and functional levels; secondly, the possibility of retrofitting existing buildings is provided. There are also famous ATC and FEMA regulations in this field. In this research, the performance of steel structure with eccentric braced FRAMEs being affected by sequence earthquakes has been studied. To do so, low-rise buildings of 3, 5, and 7 stories have been analyzed in terms of time history dynamics by nonlinear software of Perform 3D. By drawing the fragility curve of structures at different levels of performance, the seismic vulnerability of structures has been investigated. The results indicate that as the number of stories increases, the seismic vulnerability of the structure decreases, and the probability of failure in Far-field earthquakes is higher than near-fault earthquakes. In a seismic sequence discussion, the second earthquake is often affected by the fact that its PGA is larger than the first earthquake. In other words, when the PGA is the second earthquake smaller than or equal to the first earthquake, its effect on structures is very slight, which can be ignored. With regard to the fragility curves achieved, it can be concluded that the structure at the level of the safety of life (LS), which is the standard 2800 and the topic of the tenth subject of the national building regulations, has a good performance, and the design based on them is reliable.

Parabolic scaling and anisotropic dilation form the core of famous multi-resolution transformations such as curvelet and SHEARLET, which are widely used in signal processing applications like denoising. These non-adaptive geometrical wavelets are commonly used to extract structures and geometrical features of multi-dimensional signals and preserve them in noise removal treatments. In discrete setups, it is shown that SHEARLETs can outperform other rivals since in addition to scaling, they are formed by shear operator which can fully remain on integer grid. However, the redundancy of multidimensional SHEARLET transform exponentially grows with respect to the number of dimensions which in turn leads to the exponential computational and space complexity. This, seriously limits the applicability of SHEARLET transform in higher dimensions. In contrast, separable transforms process each dimension of data independent of other dimensions which result in missing the informative relations among different dimensions of the data. Therefore, in this paper a modified discrete SHEARLET transform is proposed which can overcome the redundancy and complexity issues of the classical transform. It makes a better tradeoff between completeness of the analysis achieved by processing full relations among dimensions on one hand and the redundancy and computational complexity of the resulting transform on the other hand. In fact, how dilation matrix is decomposed and block diagonalized, gives a tuning parameter for the amount of inter dimension analysis which may be used to control computation complexity and also redundancy of the resultant transform. In the context of video denoising, three different decompositions are proposed for 3x3 dilation matrix. In each block diagonalization of this dilation matrix, one dimension is separated and the other two constitute a 2D SHEARLET transform. The three block SHEARLET transforms are computed for the input data up to three levels and the resultant coefficients are treated with automatically adjusted thresholds. The output is obtained via an aggregation mechanism which combine the result of reconstruction of these three transforms. Using experiments on standard set of videos at different levels of noise, we show that the proposed approach can get very near to the quality of full 3D SHEARLET analysis while it keeps the computational complexity (time and space) comparable to the 2D SHEARLET transform.

This paper is an investigation ofL-DUAL FRAMEs with respect to a function-valued inner product, the so calledL-bracket product on L2(G), where G is a locally compact abelian group with a uniform latticeL. We show that several well known theorems for DUAL FRAMEs and DUAL Riesz bases in a Hilbert space remain valid forL-DUAL FRAMEs and L-DUAL Riesz bases in L2(G).

Steel Plate Shear Wall (SPSW) is an emerging seismic load-resistant system that, compared to other systems, enjoys the advantages of stable ductile behavior, fewer detailing requirements, rapid constructability, and economy. American seismic provisions decree that a SPSW should be designed as a moment FRAME with a web infill plate. Specifically, in case of buildings taller than 160 ft, it decrees that a DUAL system must be used. This paper presents a method of Performance-Based Plastic Design (PBPD) to design steel moment FRAME-SPSW as a DUAL lateral load-resisting system. PBPD method uses pre-selected target drift and yield mechanism as its main criteria. For a specified hazard level, the design base shear is calculated based on energy work balance method, employing pre-selected target drift. Plastic design of DUAL FRAME system has been performed to meet the pre-selected yield mechanism. As presented in the paper, design procedure involves solving a system of five equations with five variables to determine the proportion of SPSW and moment FRAME shear, shear wall thickness, and beam/ column sections. It has been considered that a four-story structure is designed with the proposed method. Seismic performance of this DUAL FRAME system, designed with the proposed method, is evaluated by nonlinear static and dynamic analysis for both Design Basis Earthquake (DBE) and Maximum Credible Earthquake (MCE). Result analysis is in accord with the assumptions, satisfying all the performance objectives. PBPD is a direct design method in which no iteration is needed to achieve the performance objectives. Determining the proportion of SPSW and moment FRAME shear is an exclusive capability of this procedure.

This article presents an optimization problem for accomplishing seismic design of Reinforced Concrete (RC) DUAL systems and RC FRAMEs. The charged system search algorithm is chosen for the optimization. An efficient structural modeling is also presented for this purpose. Here, first databases are constructed according to ACI seismic design criteria for beams, columns and shear walls. Formulations for optimum seismic design of DUAL systems (shear wall-FRAME) are proposed. With some manipulations on these formulations, optimal seismic design of RC moment resisting FRAMEs is also performed. This procedure is together with ordinary design constraints and principal seismic design constraints. These constraints consist of beams, columns, shear wall design criteria, and some seismic design provisions. Cost of the structure is defined as the objective function.Based on the results of the design examples, the proposed methodology can be considered as a suitable practical approach for optimal seismic design of reinforced concrete moment resisting FRAMEs and DUAL structural systems consisting of structural wall.